What is a Markov chain and how can it be used in creating artificial intelligence?
A Markov model includes the probability of transitioning to each state considering the current state. "Each state" may be just one point - whether it rained on specific day, for instance - or it might look like multiple things - like a pair of words. You've probably seen automatically generated weird text that almost makes sense, like Garkov (the output of a Markov model based on the Garfield comic strips). That Coding Horror article also mentions the applications of Markov techniques to Google's PageRank.

Markov models are really only powerful when they have a lot of input to work with. If a machine looked through a lot of English text, it would get a pretty good idea of what words generally come after other words. Or after looking through someone's location history, it could figure out where that person is likely to go next from a certain place. Constantly updating the "input corpus" as more data is received would let the machine tune the probabilities of all the state transitions.

Genetic algorithms are fairly different things. They create functions by shuffling around parts of functions and seeing how good each function is at a certain task. A child algorithm will depend on its parents, but Markov models are interested mostly in predicting what thing will come next in a sequence, not creating a new chunk of code. You might be able to use a Markov model to spit out a candidate function, though, depending on how simple the "alphabet" is. You could even then give more weight to the transitions in successful algorithms.